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Math Help - Group Theory: Proof on abelian and isomorphic groups.

  1. #1
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    Group Theory: Proof on abelian and isomorphic groups.

    If a function f, defined f(g)=g^-1 maps a group G to G, is isomorphic, then G is abelian.

    How do I go about proving this one?
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  2. #2
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    Let a,b\in G, then

    ab=f((ab)^{-1})=f(b^{-1}a^{-1})=f(b^{-1})f(a^{-1})=ba

    thus G is abelian
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